Metamaterials and Transformation Optics

Metamaterial is not a well-defined terminology. In fact, this terminology does not mean any specific material, but instead a new way of thinking. Usually this term means carefully engineered material structures composed of carefully designed inclusions that can exhibit unusual electromagnetic properties not inherent in the individual constituent components [1]. These properties include, for example, artificial magnetism [2], negative permeability [3], negative index of refraction [4], and hyperbolic dispersion [5, 6]. These properties lead to many fascinating phenomena such as negative refraction of light [7], sub-wavelength imaging [8], field enhancement [9], and evanescent-to-propagating wave mode conversion [5, 6], etc. Novel devices such as superlens [8–10], hyperlens [5, 6], invisibility cloak [11, 12], and plasmonic waveguide [13] based on these ideas have been designed, fabricated, and tested in the last decade. The original purpose of initiating metamaterials research might be to construct artificial structures that can respond to electromagnetic waves intensively at any frequency we desire [2]. After this goal had been achieved, researchers then made a metallic periodic structure which behaves like an effective medium for EM waves having both negative permittivity [14] and negative permeability [3], and hence has a negative refractive index [4], realizing the ‘bending light to the wrong way’ phenomena predicted by V. G. Veselago more than 4 decades ago [7]. Furthermore, Pendry pointed out that a slab of negative refraction medium having appropriate negative permittivity and permeability not only cancels the phase accumulation of propagating waves but also amplifies the evanescent